NOMBRES - Curiosités, théorie et usages

 

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Références

 

Débutants

Nombre

 

INDEX

Tables

 

TABLES de NOMBRES

 

Glossaire

Nombre

 

 

 

NOMBRES

somme de Premiers consécutifs

 

On donne les nombres premiers consécutifs et, en final, leur somme.

 

Pour tous les nombres n:

*    Somme de 2 à   5 premiers pour n  jusqu'à    1000 >>>

*    Somme de 6 à 12 premiers pour n  jusqu'à      100 >>>

 

*     Somme des k premiers nombres premiers >>>

*     Somme de 1 à 5 premiers à la puissance 1 à 5 >>>

*     Somm des k premiers nombres premiers à la puissance 1 à 5 >>>

Anglais: sum of a run of consecutive prime numbers

Les nombres marqués en rouge sont reportés dans le dictionnaire

 

 

Somme des premiers de 1 à p

 

Somme des nombres premiers

Cas de divisibilités singulières.

P = 71 divise la somme des premiers jusqu'à 71. En effet:  639 = 71 x 9

Même propriété pour P = 2 et P = 5.

Le suivant après 71 est: 369 119.

 

Somme de tous les nombres

Tous les nombres impairs divisent la somme des nombres inférieurs à eux (ou avec eux compris).

 

Somme des nombres composés

Les seuls cas (1, 22 et 25) jusqu'au prochain composé: 2 745.

 

Table des nombres premiers, leur rang (r), le cumul de la somme et ce cumul divisé par P.

Exemple de lecture: le 4e nombre premier (5) divise la somme des nombres premiers jusqu'a 5 (10).

 

 

 

Moyenne de la somme des premiers consécutifs

 

On note les cas où cette moyenne est un nombre entier.

Par exemple, la somme des 23 premiers nombres premiers 2 + 3 + 5 + … + 83 = 874 et la moyenne est 874 / 23 = 38, qui est un nombre entier.

 

 

Les cinq premières valeurs

La suite

1, 23, 53, 853, 11869, 117267, 339615, 3600489, 96643287, 2664167025, 43435512311, 501169672991, 745288471601 …

 

Voir Nombres composés

 

 

 

 

Années comme somme de premiers consécutifs

Exemple de lecture

 

1980 = 137 + 138 + … + 193, une succession de Q = 12 nombres premiers commençant par PP = 137 et finissant par PD = 193.

 

Les nombres en rouge sont premiers.

 

Les nombres marqués avec un slash (/) ou absents sont composés sans être atteints par une somme de premiers consécutifs. 

 

De 1980 à 2030

 

Voir Nombre 2016

 

  

 

Table pour somme de 2, 3, 4, 5 premiers 

jusqu'à N =1000

 

Deux

Trois

Quatre

Cinq

0, 2, 2

2, 3, 5

3, 5, 8

5, 7, 12

7, 11, 18

11, 13, 24

13, 17, 30

17, 19, 36

19, 23, 42

23, 29, 52

29, 31, 60

31, 37, 68

37, 41, 78

41, 43, 84

43, 47, 90

47, 53, 100

53, 59, 112

59, 61, 120

61, 67, 128

67, 71, 138

71, 73, 144

73, 79, 152

79, 83, 162

83, 89, 172

89, 97, 186

97, 101, 198

101, 103, 204

103, 107, 210

107, 109, 216

109, 113, 222

113, 127, 240

127, 131, 258

131, 137, 268

137, 139, 276

139, 149, 288

149, 151, 300

151, 157, 308

157, 163, 320

163, 167, 330

167, 173, 340

173, 179, 352

179, 181, 360

181, 191, 372

191, 193, 384

193, 197, 390

197, 199, 396

199, 211, 410

211, 223, 434

223, 227, 450

227, 229, 456

229, 233, 462

233, 239, 472

239, 241, 480

241, 251, 492

251, 257, 508

257, 263, 520

263, 269, 532

269, 271, 540

271, 277, 548

277, 281, 558

281, 283, 564

283, 293, 576

293, 307, 600

307, 311, 618

311, 313, 624

313, 317, 630

317, 331, 648

331, 337, 668

337, 347, 684

347, 349, 696

349, 353, 702

353, 359, 712

359, 367, 726

367, 373, 740

373, 379, 752

379, 383, 762

383, 389, 772

389, 397, 786

397, 401, 798

401, 409, 810

409, 419, 828

419, 421, 840

421, 431, 852

431, 433, 864

433, 439, 872

439, 443, 882

443, 449, 892

449, 457, 906

457, 461, 918

461, 463, 924

463, 467, 930

467, 479, 946

479, 487, 966

487, 491, 978

491, 499, 990

499, 503, 1002

503, 509, 1012

509, 521, 1030

521, 523, 1044

523, 541, 1064

541, 547, 1088

547, 557, 1104

557, 563, 1120

563, 569, 1132

569, 571, 1140

571, 577, 1148

577, 587, 1164

587, 593, 1180

593, 599, 1192

599, 601, 1200

601, 607, 1208

607, 613, 1220

613, 617, 1230

617, 619, 1236

619, 631, 1250

631, 641, 1272

641, 643, 1284

643, 647, 1290

647, 653, 1300

653, 659, 1312

659, 661, 1320

661, 673, 1334

673, 677, 1350

677, 683, 1360

683, 691, 1374

691, 701, 1392

701, 709, 1410

709, 719, 1428

719, 727, 1446

727, 733, 1460

733, 739, 1472

739, 743, 1482

743, 751, 1494

751, 757, 1508

757, 761, 1518

761, 769, 1530

769, 773, 1542

773, 787, 1560

787, 797, 1584

797, 809, 1606

809, 811, 1620

811, 821, 1632

821, 823, 1644

823, 827, 1650

827, 829, 1656

829, 839, 1668

839, 853, 1692

853, 857, 1710

857, 859, 1716

859, 863, 1722

863, 877, 1740

877, 881, 1758

881, 883, 1764

883, 887, 1770

887, 907, 1794

907, 911, 1818

911, 919, 1830

919, 929, 1848

929, 937, 1866

937, 941, 1878

941, 947, 1888

947, 953, 1900

953, 967, 1920

967, 971, 1938

971, 977, 1948

977, 983, 1960

983, 991, 1974

991, 997, 1988

 

0, 0, 2, 2

0, 2, 3, 5

2, 3, 5, 10

3, 5, 7, 15

5, 7, 11, 23

7, 11, 13, 31

11, 13, 17, 41

13, 17, 19, 49

17, 19, 23, 59

19, 23, 29, 71

23, 29, 31, 83

29, 31, 37, 97

31, 37, 41, 109

37, 41, 43, 121

41, 43, 47, 131

43, 47, 53, 143

47, 53, 59, 159

53, 59, 61, 173

59, 61, 67, 187

61, 67, 71, 199

67, 71, 73, 211

71, 73, 79, 223

73, 79, 83, 235

79, 83, 89, 251

83, 89, 97, 269

89, 97, 101, 287

97, 101, 103, 301

101, 103, 107, 311

103, 107, 109, 319

107, 109, 113, 329

109, 113, 127, 349

113, 127, 131, 371

127, 131, 137, 395

131, 137, 139, 407

137, 139, 149, 425

139, 149, 151, 439

149, 151, 157, 457

151, 157, 163, 471

157, 163, 167, 487

163, 167, 173, 503

167, 173, 179, 519

173, 179, 181, 533

179, 181, 191, 551

181, 191, 193, 565

191, 193, 197, 581

193, 197, 199, 589

197, 199, 211, 607

199, 211, 223, 633

211, 223, 227, 661

223, 227, 229, 679

227, 229, 233, 689

229, 233, 239, 701

233, 239, 241, 713

239, 241, 251, 731

241, 251, 257, 749

251, 257, 263, 771

257, 263, 269, 789

263, 269, 271, 803

269, 271, 277, 817

271, 277, 281, 829

277, 281, 283, 841

281, 283, 293, 857

283, 293, 307, 883

293, 307, 311, 911

307, 311, 313, 931

311, 313, 317, 941

313, 317, 331, 961

317, 331, 337, 985

331, 337, 347, 1015

337, 347, 349, 1033

347, 349, 353, 1049

349, 353, 359, 1061

353, 359, 367, 1079

359, 367, 373, 1099

367, 373, 379, 1119

373, 379, 383, 1135

379, 383, 389, 1151

383, 389, 397, 1169

389, 397, 401, 1187

397, 401, 409, 1207

401, 409, 419, 1229

409, 419, 421, 1249

419, 421, 431, 1271

421, 431, 433, 1285

431, 433, 439, 1303

433, 439, 443, 1315

439, 443, 449, 1331

443, 449, 457, 1349

449, 457, 461, 1367

457, 461, 463, 1381

461, 463, 467, 1391

463, 467, 479, 1409

467, 479, 487, 1433

479, 487, 491, 1457

487, 491, 499, 1477

491, 499, 503, 1493

499, 503, 509, 1511

503, 509, 521, 1533

509, 521, 523, 1553

521, 523, 541, 1585

523, 541, 547, 1611

541, 547, 557, 1645

547, 557, 563, 1667

557, 563, 569, 1689

563, 569, 571, 1703

569, 571, 577, 1717

571, 577, 587, 1735

577, 587, 593, 1757

587, 593, 599, 1779

593, 599, 601, 1793

599, 601, 607, 1807

601, 607, 613, 1821

607, 613, 617, 1837

613, 617, 619, 1849

617, 619, 631, 1867

619, 631, 641, 1891

631, 641, 643, 1915

641, 643, 647, 1931

643, 647, 653, 1943

647, 653, 659, 1959

653, 659, 661, 1973

659, 661, 673, 1993

661, 673, 677, 2011

673, 677, 683, 2033

677, 683, 691, 2051

683, 691, 701, 2075

691, 701, 709, 2101

701, 709, 719, 2129

709, 719, 727, 2155

719, 727, 733, 2179

727, 733, 739, 2199

733, 739, 743, 2215

739, 743, 751, 2233

743, 751, 757, 2251

751, 757, 761, 2269

757, 761, 769, 2287

761, 769, 773, 2303

769, 773, 787, 2329

773, 787, 797, 2357

787, 797, 809, 2393

797, 809, 811, 2417

809, 811, 821, 2441

811, 821, 823, 2455

821, 823, 827, 2471

823, 827, 829, 2479

827, 829, 839, 2495

829, 839, 853, 2521

839, 853, 857, 2549

853, 857, 859, 2569

857, 859, 863, 2579

859, 863, 877, 2599

863, 877, 881, 2621

877, 881, 883, 2641

881, 883, 887, 2651

883, 887, 907, 2677

887, 907, 911, 2705

907, 911, 919, 2737

911, 919, 929, 2759

919, 929, 937, 2785

929, 937, 941, 2807

937, 941, 947, 2825

941, 947, 953, 2841

947, 953, 967, 2867

953, 967, 971, 2891

967, 971, 977, 2915

971, 977, 983, 2931

977, 983, 991, 2951

983, 991, 997, 2971

 

0, 0, 0, 2, 2

0, 0, 2, 3, 5

0, 2, 3, 5, 10

2, 3, 5, 7, 17

3, 5, 7, 11, 26

5, 7, 11, 13, 36

7, 11, 13, 17, 48

11, 13, 17, 19, 60

13, 17, 19, 23, 72

17, 19, 23, 29, 88

19, 23, 29, 31, 102

23, 29, 31, 37, 120

29, 31, 37, 41, 138

31, 37, 41, 43, 152

37, 41, 43, 47, 168

41, 43, 47, 53, 184

43, 47, 53, 59, 202

47, 53, 59, 61, 220

53, 59, 61, 67, 240

59, 61, 67, 71, 258

61, 67, 71, 73, 272

67, 71, 73, 79, 290

71, 73, 79, 83, 306

73, 79, 83, 89, 324

79, 83, 89, 97, 348

83, 89, 97, 101, 370

89, 97, 101, 103, 390

97, 101, 103, 107, 408

101, 103, 107, 109, 420

103, 107, 109, 113, 432

107, 109, 113, 127, 456

109, 113, 127, 131, 480

113, 127, 131, 137, 508

127, 131, 137, 139, 534

131, 137, 139, 149, 556

137, 139, 149, 151, 576

139, 149, 151, 157, 596

149, 151, 157, 163, 620

151, 157, 163, 167, 638

157, 163, 167, 173, 660

163, 167, 173, 179, 682

167, 173, 179, 181, 700

173, 179, 181, 191, 724

179, 181, 191, 193, 744

181, 191, 193, 197, 762

191, 193, 197, 199, 780

193, 197, 199, 211, 800

197, 199, 211, 223, 830

199, 211, 223, 227, 860

211, 223, 227, 229, 890

223, 227, 229, 233, 912

227, 229, 233, 239, 928

229, 233, 239, 241, 942

233, 239, 241, 251, 964

239, 241, 251, 257, 988

241, 251, 257, 263, 1012

251, 257, 263, 269, 1040

257, 263, 269, 271, 1060

263, 269, 271, 277, 1080

269, 271, 277, 281, 1098

271, 277, 281, 283, 1112

277, 281, 283, 293, 1134

281, 283, 293, 307, 1164

283, 293, 307, 311, 1194

293, 307, 311, 313, 1224

307, 311, 313, 317, 1248

311, 313, 317, 331, 1272

313, 317, 331, 337, 1298

317, 331, 337, 347, 1332

331, 337, 347, 349, 1364

337, 347, 349, 353, 1386

347, 349, 353, 359, 1408

349, 353, 359, 367, 1428

353, 359, 367, 373, 1452

359, 367, 373, 379, 1478

367, 373, 379, 383, 1502

373, 379, 383, 389, 1524

379, 383, 389, 397, 1548

383, 389, 397, 401, 1570

389, 397, 401, 409, 1596

397, 401, 409, 419, 1626

401, 409, 419, 421, 1650

409, 419, 421, 431, 1680

419, 421, 431, 433, 1704

421, 431, 433, 439, 1724

431, 433, 439, 443, 1746

433, 439, 443, 449, 1764

439, 443, 449, 457, 1788

443, 449, 457, 461, 1810

449, 457, 461, 463, 1830

457, 461, 463, 467, 1848

461, 463, 467, 479, 1870

463, 467, 479, 487, 1896

467, 479, 487, 491, 1924

479, 487, 491, 499, 1956

487, 491, 499, 503, 1980

491, 499, 503, 509, 2002

499, 503, 509, 521, 2032

503, 509, 521, 523, 2056

509, 521, 523, 541, 2094

521, 523, 541, 547, 2132

523, 541, 547, 557, 2168

541, 547, 557, 563, 2208

547, 557, 563, 569, 2236

557, 563, 569, 571, 2260

563, 569, 571, 577, 2280

569, 571, 577, 587, 2304

571, 577, 587, 593, 2328

577, 587, 593, 599, 2356

587, 593, 599, 601, 2380

593, 599, 601, 607, 2400

599, 601, 607, 613, 2420

601, 607, 613, 617, 2438

607, 613, 617, 619, 2456

613, 617, 619, 631, 2480

617, 619, 631, 641, 2508

619, 631, 641, 643, 2534

631, 641, 643, 647, 2562

641, 643, 647, 653, 2584

643, 647, 653, 659, 2602

647, 653, 659, 661, 2620

653, 659, 661, 673, 2646

659, 661, 673, 677, 2670

661, 673, 677, 683, 2694

673, 677, 683, 691, 2724

677, 683, 691, 701, 2752

683, 691, 701, 709, 2784

691, 701, 709, 719, 2820

701, 709, 719, 727, 2856

709, 719, 727, 733, 2888

719, 727, 733, 739, 2918

727, 733, 739, 743, 2942

733, 739, 743, 751, 2966

739, 743, 751, 757, 2990

743, 751, 757, 761, 3012

751, 757, 761, 769, 3038

757, 761, 769, 773, 3060

761, 769, 773, 787, 3090

769, 773, 787, 797, 3126

773, 787, 797, 809, 3166

787, 797, 809, 811, 3204

797, 809, 811, 821, 3238

809, 811, 821, 823, 3264

811, 821, 823, 827, 3282

821, 823, 827, 829, 3300

823, 827, 829, 839, 3318

827, 829, 839, 853, 3348

829, 839, 853, 857, 3378

839, 853, 857, 859, 3408

853, 857, 859, 863, 3432

857, 859, 863, 877, 3456

859, 863, 877, 881, 3480

863, 877, 881, 883, 3504

877, 881, 883, 887, 3528

881, 883, 887, 907, 3558

883, 887, 907, 911, 3588

887, 907, 911, 919, 3624

907, 911, 919, 929, 3666

911, 919, 929, 937, 3696

919, 929, 937, 941, 3726

929, 937, 941, 947, 3754

937, 941, 947, 953, 3778

941, 947, 953, 967, 3808

947, 953, 967, 971, 3838

953, 967, 971, 977, 3868

967, 971, 977, 983, 3898

971, 977, 983, 991, 3922

977, 983, 991, 997, 3948

 

0, 0, 0, 0, 2, 2

0, 0, 0, 2, 3, 5

0, 0, 2, 3, 5, 10

0, 2, 3, 5, 7, 17

2, 3, 5, 7, 11, 28

3, 5, 7, 11, 13, 39

5, 7, 11, 13, 17, 53

7, 11, 13, 17, 19, 67

11, 13, 17, 19, 23, 83

13, 17, 19, 23, 29, 101

17, 19, 23, 29, 31, 119

19, 23, 29, 31, 37, 139

23, 29, 31, 37, 41, 161

29, 31, 37, 41, 43, 181

31, 37, 41, 43, 47, 199

37, 41, 43, 47, 53, 221

41, 43, 47, 53, 59, 243

43, 47, 53, 59, 61, 263

47, 53, 59, 61, 67, 287

53, 59, 61, 67, 71, 311

59, 61, 67, 71, 73, 331

61, 67, 71, 73, 79, 351

67, 71, 73, 79, 83, 373

71, 73, 79, 83, 89, 395

73, 79, 83, 89, 97, 421

79, 83, 89, 97, 101, 449

83, 89, 97, 101, 103, 473

89, 97, 101, 103, 107, 497

97, 101, 103, 107, 109, 517

101, 103, 107, 109, 113, 533

103, 107, 109, 113, 127, 559

107, 109, 113, 127, 131, 587

109, 113, 127, 131, 137, 617

113, 127, 131, 137, 139, 647

127, 131, 137, 139, 149, 683

131, 137, 139, 149, 151, 707

137, 139, 149, 151, 157, 733

139, 149, 151, 157, 163, 759

149, 151, 157, 163, 167, 787

151, 157, 163, 167, 173, 811

157, 163, 167, 173, 179, 839

163, 167, 173, 179, 181, 863

167, 173, 179, 181, 191, 891

173, 179, 181, 191, 193, 917

179, 181, 191, 193, 197, 941

181, 191, 193, 197, 199, 961

191, 193, 197, 199, 211, 991

193, 197, 199, 211, 223, 1023

197, 199, 211, 223, 227, 1057

199, 211, 223, 227, 229, 1089

211, 223, 227, 229, 233, 1123

223, 227, 229, 233, 239, 1151

227, 229, 233, 239, 241, 1169

229, 233, 239, 241, 251, 1193

233, 239, 241, 251, 257, 1221

239, 241, 251, 257, 263, 1251

241, 251, 257, 263, 269, 1281

251, 257, 263, 269, 271, 1311

257, 263, 269, 271, 277, 1337

263, 269, 271, 277, 281, 1361

269, 271, 277, 281, 283, 1381

271, 277, 281, 283, 293, 1405

277, 281, 283, 293, 307, 1441

281, 283, 293, 307, 311, 1475

283, 293, 307, 311, 313, 1507

293, 307, 311, 313, 317, 1541

307, 311, 313, 317, 331, 1579

311, 313, 317, 331, 337, 1609

313, 317, 331, 337, 347, 1645

317, 331, 337, 347, 349, 1681

331, 337, 347, 349, 353, 1717

337, 347, 349, 353, 359, 1745

347, 349, 353, 359, 367, 1775

349, 353, 359, 367, 373, 1801

353, 359, 367, 373, 379, 1831

359, 367, 373, 379, 383, 1861

367, 373, 379, 383, 389, 1891

373, 379, 383, 389, 397, 1921

379, 383, 389, 397, 401, 1949

383, 389, 397, 401, 409, 1979

389, 397, 401, 409, 419, 2015

397, 401, 409, 419, 421, 2047

401, 409, 419, 421, 431, 2081

409, 419, 421, 431, 433, 2113

419, 421, 431, 433, 439, 2143

421, 431, 433, 439, 443, 2167

431, 433, 439, 443, 449, 2195

433, 439, 443, 449, 457, 2221

439, 443, 449, 457, 461, 2249

443, 449, 457, 461, 463, 2273

449, 457, 461, 463, 467, 2297

457, 461, 463, 467, 479, 2327

461, 463, 467, 479, 487, 2357

463, 467, 479, 487, 491, 2387

467, 479, 487, 491, 499, 2423

479, 487, 491, 499, 503, 2459

487, 491, 499, 503, 509, 2489

491, 499, 503, 509, 521, 2523

499, 503, 509, 521, 523, 2555

503, 509, 521, 523, 541, 2597

509, 521, 523, 541, 547, 2641

521, 523, 541, 547, 557, 2689

523, 541, 547, 557, 563, 2731

541, 547, 557, 563, 569, 2777

547, 557, 563, 569, 571, 2807

557, 563, 569, 571, 577, 2837

563, 569, 571, 577, 587, 2867

569, 571, 577, 587, 593, 2897

571, 577, 587, 593, 599, 2927

577, 587, 593, 599, 601, 2957

587, 593, 599, 601, 607, 2987

593, 599, 601, 607, 613, 3013

599, 601, 607, 613, 617, 3037

601, 607, 613, 617, 619, 3057

607, 613, 617, 619, 631, 3087

613, 617, 619, 631, 641, 3121

617, 619, 631, 641, 643, 3151

619, 631, 641, 643, 647, 3181

631, 641, 643, 647, 653, 3215

641, 643, 647, 653, 659, 3243

643, 647, 653, 659, 661, 3263

647, 653, 659, 661, 673, 3293

653, 659, 661, 673, 677, 3323

659, 661, 673, 677, 683, 3353

661, 673, 677, 683, 691, 3385

673, 677, 683, 691, 701, 3425

677, 683, 691, 701, 709, 3461

683, 691, 701, 709, 719, 3503

691, 701, 709, 719, 727, 3547

701, 709, 719, 727, 733, 3589

709, 719, 727, 733, 739, 3627

719, 727, 733, 739, 743, 3661

727, 733, 739, 743, 751, 3693

733, 739, 743, 751, 757, 3723

739, 743, 751, 757, 761, 3751

743, 751, 757, 761, 769, 3781

751, 757, 761, 769, 773, 3811

757, 761, 769, 773, 787, 3847

761, 769, 773, 787, 797, 3887

769, 773, 787, 797, 809, 3935

773, 787, 797, 809, 811, 3977

787, 797, 809, 811, 821, 4025

797, 809, 811, 821, 823, 4061

809, 811, 821, 823, 827, 4091

811, 821, 823, 827, 829, 4111

821, 823, 827, 829, 839, 4139

823, 827, 829, 839, 853, 4171

827, 829, 839, 853, 857, 4205

829, 839, 853, 857, 859, 4237

839, 853, 857, 859, 863, 4271

853, 857, 859, 863, 877, 4309

857, 859, 863, 877, 881, 4337

859, 863, 877, 881, 883, 4363

863, 877, 881, 883, 887, 4391

877, 881, 883, 887, 907, 4435

881, 883, 887, 907, 911, 4469

883, 887, 907, 911, 919, 4507

887, 907, 911, 919, 929, 4553

907, 911, 919, 929, 937, 4603

911, 919, 929, 937, 941, 4637

919, 929, 937, 941, 947, 4673

929, 937, 941, 947, 953, 4707

937, 941, 947, 953, 967, 4745

941, 947, 953, 967, 971, 4779

947, 953, 967, 971, 977, 4815

953, 967, 971, 977, 983, 4851

967, 971, 977, 983, 991, 4889

971, 977, 983, 991, 997, 4919

 

 

 

Table pour 6, 7, 8, 9, 10, 11, 12  jusqu'à 100

Six

Sept

Huit

2, 3, 5, 7, 11, 13, 41

3, 5, 7, 11, 13, 17, 56

5, 7, 11, 13, 17, 19, 72

7, 11, 13, 17, 19, 23, 90

11, 13, 17, 19, 23, 29, 112

13, 17, 19, 23, 29, 31, 132

17, 19, 23, 29, 31, 37, 156

19, 23, 29, 31, 37, 41, 180

23, 29, 31, 37, 41, 43, 204

29, 31, 37, 41, 43, 47, 228

31, 37, 41, 43, 47, 53, 252

37, 41, 43, 47, 53, 59, 280

41, 43, 47, 53, 59, 61, 304

43, 47, 53, 59, 61, 67, 330

47, 53, 59, 61, 67, 71, 358

53, 59, 61, 67, 71, 73, 384

59, 61, 67, 71, 73, 79, 410

61, 67, 71, 73, 79, 83, 434

67, 71, 73, 79, 83, 89, 462

71, 73, 79, 83, 89, 97, 492

 

2, 3, 5, 7, 11, 13, 17, 58

3, 5, 7, 11, 13, 17, 19, 75

5, 7, 11, 13, 17, 19, 23, 95

7, 11, 13, 17, 19, 23, 29, 119

11, 13, 17, 19, 23, 29, 31, 143

13, 17, 19, 23, 29, 31, 37, 169

17, 19, 23, 29, 31, 37, 41, 197

19, 23, 29, 31, 37, 41, 43, 223

23, 29, 31, 37, 41, 43, 47, 251

29, 31, 37, 41, 43, 47, 53, 281

31, 37, 41, 43, 47, 53, 59, 311

37, 41, 43, 47, 53, 59, 61, 341

41, 43, 47, 53, 59, 61, 67, 371

43, 47, 53, 59, 61, 67, 71, 401

47, 53, 59, 61, 67, 71, 73, 431

53, 59, 61, 67, 71, 73, 79, 463

59, 61, 67, 71, 73, 79, 83, 493

61, 67, 71, 73, 79, 83, 89, 523

67, 71, 73, 79, 83, 89, 97, 559

 

2, 3, 5, 7, 11, 13, 17, 19, 77

3, 5, 7, 11, 13, 17, 19, 23, 98

5, 7, 11, 13, 17, 19, 23, 29, 124

7, 11, 13, 17, 19, 23, 29, 31, 150

11, 13, 17, 19, 23, 29, 31, 37, 180

13, 17, 19, 23, 29, 31, 37, 41, 210

17, 19, 23, 29, 31, 37, 41, 43, 240

19, 23, 29, 31, 37, 41, 43, 47, 270

23, 29, 31, 37, 41, 43, 47, 53, 304

29, 31, 37, 41, 43, 47, 53, 59, 340

31, 37, 41, 43, 47, 53, 59, 61, 372

37, 41, 43, 47, 53, 59, 61, 67, 408

41, 43, 47, 53, 59, 61, 67, 71, 442

43, 47, 53, 59, 61, 67, 71, 73, 474

47, 53, 59, 61, 67, 71, 73, 79, 510

53, 59, 61, 67, 71, 73, 79, 83, 546

59, 61, 67, 71, 73, 79, 83, 89, 582

61, 67, 71, 73, 79, 83, 89, 97, 620

 

 

Neuf

Dix

2, 3, 5, 7, 11, 13, 17, 19, 23, 100

3, 5, 7, 11, 13, 17, 19, 23, 29, 127

5, 7, 11, 13, 17, 19, 23, 29, 31, 155

7, 11, 13, 17, 19, 23, 29, 31, 37, 187

11, 13, 17, 19, 23, 29, 31, 37, 41, 221

13, 17, 19, 23, 29, 31, 37, 41, 43, 253

17, 19, 23, 29, 31, 37, 41, 43, 47, 287

19, 23, 29, 31, 37, 41, 43, 47, 53, 323

23, 29, 31, 37, 41, 43, 47, 53, 59, 363

29, 31, 37, 41, 43, 47, 53, 59, 61, 401

31, 37, 41, 43, 47, 53, 59, 61, 67, 439

37, 41, 43, 47, 53, 59, 61, 67, 71, 479

41, 43, 47, 53, 59, 61, 67, 71, 73, 515

43, 47, 53, 59, 61, 67, 71, 73, 79, 553

47, 53, 59, 61, 67, 71, 73, 79, 83, 593

53, 59, 61, 67, 71, 73, 79, 83, 89, 635

59, 61, 67, 71, 73, 79, 83, 89, 97, 679

 

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 129

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 158

5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 192

7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 228

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 264

13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 300

17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 340

19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 382

23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 424

29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 468

31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 510

37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 552

41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 594

43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 636

47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 682

53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 732

 

 

Onze

Douze

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 160

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 195

5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 233

7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 271

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 311

13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 353

17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 399

19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 443

23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 491

29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 539

31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 583

37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 631

41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 677

43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 725

47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 779

 

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 197

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 236

5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 276

7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 318

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 364

13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 412

17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 460

19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 510

23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 562

29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 612

31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 662

37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 714

41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 766

43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 822

 

 

 

Treize

Quatorze

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 238

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 279

5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 323

7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 371

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 423

13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 473

17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 527

19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 581

23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 635

29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 691

31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 745

37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 803

41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 863

 

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 281

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 326

5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 376

7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 430

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 484

13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 540

17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 598

19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 654

23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 714

29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 774

31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 834

37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 900

 

 

 

Quinze

Seize

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 328

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 379

5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 435

7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 491

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 551

13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 611

17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 671

19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 733

23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 797

29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 863

31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 931

 

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 381

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 438

5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 496

7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 558

11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 622

13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 684

17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 750

19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 816

23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 886

29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 960

 

 

Somme des k premiers nombres premiers

 

Exemples en rouge pour les sommes de 16 premiers telles qu'indiquées dans la table juste au-dessus.

Somme S de k premier, le dernier étant n.

 

TOUS

k, n, S

1, 2, 2

2, 3, 5

3, 5, 10

4, 7, 17

5, 11, 28

6, 13, 41

7, 17, 58

8, 19, 77

9, 23, 100

10, 29, 129

11, 31, 160

12, 37, 197

13, 41, 238

14, 43, 281

15, 47, 328

16, 53, 381

17, 59, 440

18, 61, 501

19, 67, 568

20, 71, 639

21, 73, 712

22, 79, 791

23, 83, 874

24, 89, 963

25, 97, 1060

26, 101, 1161

27, 103, 1264

28, 107, 1371

29, 109, 1480

30, 113, 1593

31, 127, 1720

32, 131, 1851

33, 137, 1988

34, 139, 2127

35, 149, 2276

36, 151, 2427

37, 157, 2584

38, 163, 2747

39, 167, 2914

40, 173, 3087

41, 179, 3266

42, 181, 3447

43, 191, 3638

44, 193, 3831

45, 197, 4028

46, 199, 4227

47, 211, 4438

48, 223, 4661

49, 227, 4888

50, 229, 5117

51, 233, 5350

52, 239, 5589

53, 241, 5830

54, 251, 6081

55, 257, 6338

56, 263, 6601

57, 269, 6870

58, 271, 7141

59, 277, 7418

60, 281, 7699

61, 283, 7982

62, 293, 8275

63, 307, 8582

64, 311, 8893

65, 313, 9206

66, 317, 9523

67, 331, 9854

68, 337, 10191

69, 347, 10538

70, 349, 10887

71, 353, 11240

72, 359, 11599

73, 367, 11966

74, 373, 12339

75, 379, 12718

76, 383, 13101

77, 389, 13490

78, 397, 13887

79, 401, 14288

80, 409, 14697

81, 419, 15116

82, 421, 15537

83, 431, 15968

84, 433, 16401

85, 439, 16840

86, 443, 17283

87, 449, 17732

88, 457, 18189

89, 461, 18650

90, 463, 19113

91, 467, 19580

92, 479, 20059

93, 487, 20546

94, 491, 21037

95, 499, 21536

96, 503, 22039

97, 509, 22548

98, 521, 23069

99, 523, 23592

100, 541, 24133

101, 547, 24680

102, 557, 25237

103, 563, 25800

104, 569, 26369

105, 571, 26940

106, 577, 27517

107, 587, 28104

108, 593, 28697

109, 599, 29296

110, 601, 29897

111, 607, 30504

112, 613, 31117

113, 617, 31734

114, 619, 32353

115, 631, 32984

116, 641, 33625

117, 643, 34268

118, 647, 34915

119, 653, 35568

120, 659, 36227

121, 661, 36888

122, 673, 37561

123, 677, 38238

124, 683, 38921

125, 691, 39612

126, 701, 40313

127, 709, 41022

128, 719, 41741

129, 727, 42468

130, 733, 43201

131, 739, 43940

132, 743, 44683

133, 751, 45434

134, 757, 46191

135, 761, 46952

136, 769, 47721

137, 773, 48494

138, 787, 49281

139, 797, 50078

140, 809, 50887

141, 811, 51698

142, 821, 52519

143, 823, 53342

144, 827, 54169

145, 829, 54998

146, 839, 55837

147, 853, 56690

148, 857, 57547

149, 859, 58406

150, 863, 59269

151, 877, 60146

152, 881, 61027

153, 883, 61910

154, 887, 62797

155, 907, 63704

156, 911, 64615

157, 919, 65534

158, 929, 66463

159, 937, 67400

160, 941, 68341

161, 947, 69288

162, 953, 70241

163, 967, 71208

164, 971, 72179

165, 977, 73156

166, 983, 74139

167, 991, 75130

168, 997, 76127

169, 1009, 77136

 

IMPAIRS

k, n, S

1, 3, 3

2, 5, 8

3, 7, 15

4, 11, 26

5, 13, 39

6, 17, 56

7, 19, 75

8, 23, 98

9, 29, 127

10, 31, 158

11, 37, 195

12, 41, 236

13, 43, 279

14, 47, 326

15, 53, 379

16, 59, 438

17, 61, 499

18, 67, 566

19, 71, 637

20, 73, 710

21, 79, 789

22, 83, 872

23, 89, 961

24, 97, 1058

25, 101, 1159

26, 103, 1262

27, 107, 1369

28, 109, 1478

29, 113, 1591

30, 127, 1718

31, 131, 1849

32, 137, 1986

33, 139, 2125

34, 149, 2274

35, 151, 2425

36, 157, 2582

37, 163, 2745

38, 167, 2912

39, 173, 3085

40, 179, 3264

41, 181, 3445

42, 191, 3636

43, 193, 3829

44, 197, 4026

45, 199, 4225

46, 211, 4436

47, 223, 4659

48, 227, 4886

49, 229, 5115

50, 233, 5348

51, 239, 5587

52, 241, 5828

53, 251, 6079

54, 257, 6336

55, 263, 6599

56, 269, 6868

57, 271, 7139

58, 277, 7416

59, 281, 7697

60, 283, 7980

61, 293, 8273

62, 307, 8580

63, 311, 8891

64, 313, 9204

65, 317, 9521

66, 331, 9852

67, 337, 10189

68, 347, 10536

69, 349, 10885

70, 353, 11238

71, 359, 11597

72, 367, 11964

73, 373, 12337

74, 379, 12716

75, 383, 13099

76, 389, 13488

77, 397, 13885

78, 401, 14286

79, 409, 14695

80, 419, 15114

81, 421, 15535

82, 431, 15966

83, 433, 16399

84, 439, 16838

85, 443, 17281

86, 449, 17730

87, 457, 18187

88, 461, 18648

89, 463, 19111

90, 467, 19578

91, 479, 20057

92, 487, 20544

93, 491, 21035

94, 499, 21534

95, 503, 22037

96, 509, 22546

97, 521, 23067

98, 523, 23590

99, 541, 24131

100, 547, 24678

101, 557, 25235

102, 563, 25798

103, 569, 26367

104, 571, 26938

105, 577, 27515

106, 587, 28102

107, 593, 28695

108, 599, 29294

109, 601, 29895

110, 607, 30502

111, 613, 31115

112, 617, 31732

113, 619, 32351

114, 631, 32982

115, 641, 33623

116, 643, 34266

117, 647, 34913

118, 653, 35566

119, 659, 36225

120, 661, 36886

121, 673, 37559

122, 677, 38236

123, 683, 38919

124, 691, 39610

125, 701, 40311

126, 709, 41020

127, 719, 41739

128, 727, 42466

129, 733, 43199

130, 739, 43938

131, 743, 44681

132, 751, 45432

133, 757, 46189

134, 761, 46950

135, 769, 47719

136, 773, 48492

137, 787, 49279

138, 797, 50076

139, 809, 50885

140, 811, 51696

141, 821, 52517

142, 823, 53340

143, 827, 54167

144, 829, 54996

145, 839, 55835

146, 853, 56688

147, 857, 57545

148, 859, 58404

149, 863, 59267

150, 877, 60144

151, 881, 61025

152, 883, 61908

153, 887, 62795

154, 907, 63702

155, 911, 64613

156, 919, 65532

157, 929, 66461

158, 937, 67398

159, 941, 68339

160, 947, 69286

161, 953, 70239

162, 967, 71206

163, 971, 72177

164, 977, 73154

165, 983, 74137

166, 991, 75128

167, 997, 76125

168, 1009, 77134

 

 

Somme de 2 à 5 premiers consécutifs à la puissance 1 à 5

Exemple: 5 = 21 + 31, 13 = 22 + 32, 35 = 23 + 33… 10 = 21 + 31 + 51, 38 = 22 + 32 + 52

 

 

Somme des Q premiers consécutifs de 1 à P à la puissance 1 à 5

Exemple: Somme des cubes des quatre premiers nombres premiers = 503

23 + 33 + 53 + 73 = 503

 Tableau pour les 25 premiers jusqu'à n = 100

 

 

 

 

 

Voir

*    Développements sur les nombres premiers

*    Liste des tables de nombres

*    Nombres premiersIndex

*    Orientation vers tous les nombres du dictionnaire

*    Somme de cubes

*    Somme de premiers distincts

Sites

*    OEIS A007504 - Sum of first n primes

*    OEIS A045345 - Numbers n such that n divides sum of first n primes

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